Linear rank one preservers on tensor products of Hermitian matrices

2015/11/27 by Jinting Lau, Ming Huat Lim · 2 citations
Mathematics · Computer Science · #Advanced Topics in Algebra #Matrix Theory and Algorithms #Tensor decomposition and applications

paper · doi:10.1080/03081087.2015.1115811

Abstract

In this note, we characterize linear maps between spaces of Hermitian matrices over a field with involution which preserve the rank of the identity matrix and the rank of tensor products of rank one Hermitian matrices. It is assumed that the fixed field with respect to the field with involution has at least four elements. We also present some applications of our main result to other preserver problems.

Cited by

• Nonstandard rank-one nonincreasing maps on symmetric matrices
• Decomposability preserving linear maps between symmetric spaces

Related

• A note on linear preservers of certain ranks of tensor products of matrices
• Linear maps preserving rank of tensor products of matrices
• Linear mappings on second symmetric product spaces that Preserve rank less than or equal to one
• Linear preservers of rank k projections
• Linear maps preserving product of involutions